Bandlimited field reconstruction from samples obtained on a discrete grid with unknown random locations

Mallick, Ankur; Kumar, Animesh

doi:10.1109/icassp.2016.7472431

Cited by 3 publications

(1 citation statement)

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“…More generally, the topic of sampling with jitter on the sampling locations [3], [18], is well known in the literature. Mallick and Kumar [19] worked on reconstruction of bandlimited fields from location-unaware sensors restricted on a discrete grid. A more generic case of sampling from unknown locations coming from a known underlying distribution was introduced recently [20].…”

Section: Introductionmentioning

confidence: 99%

Spatial Field estimation from Samples taken at Unknown Locations generated by an Unknown Autoregressive Process

Salgia,

Kumar

2017

Preprint

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Sampling physical fields with mobile sensors is an upcoming field of interest. This offers greater advantages in terms of cost as often just a single sensor can be used for field sensing, can be employed almost everywhere without sensing stations, and has nominal operational costs. In a sampling scenario using mobile sensors, knowing sampling locations more accurately leads to a manifold increase in the costs. Moreover, the inertia of the moving vehicle constrains the independence between the intersample distances, making them correlated. This work, thus, aims at estimating spatially bandlimited fields from samples, corrupted with measurement noise, collected on sampling locations obtained from an autoregressive model on the intersample distances. The autoregressive model is used to capture the correlation between the intersample distances. In this setup of sampling at unknown sampling locations obtained from an autoregressive model on intersample distances, the mean squared error between the field and its estimated version has been shown to decrease as O(1/n), where n is the average number of samples taken by the moving sensor.

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Section: Introductionmentioning

confidence: 99%

Spatial Field estimation from Samples taken at Unknown Locations generated by an Unknown Autoregressive Process

Salgia,

Kumar

2017

Preprint

Self Cite

View full text Add to dashboard Cite

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Bandlimited field estimation from samples recorded by a location-unaware mobile sensor

Kumar

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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On Bandlimited Field Estimation from Samples Recorded by a Location-Unaware Mobile Sensor

Kumar

2017

IEEE Trans. Inform. Theory

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Abstract-Sampling of physical fields with mobile sensor is an emerging area. In this context, this work introduces and proposes solutions to a fundamental question: can a spatial field be estimated from samples taken at unknown sampling locations?Unknown sampling location, sample quantization, unknown bandwidth of the field, and presence of measurement-noise present difficulties in the process of field estimation. In this work, except for quantization, the other three issues will be tackled together in a mobile-sampling framework. Spatially bandlimited fields are considered. It is assumed that measurement-noise affected field samples are collected on spatial locations obtained from an unknown renewal process. That is, the samples are obtained on locations obtained from a renewal process, but the sampling locations and the renewal process distribution are unknown. In this unknown sampling location setup, it is shown that the mean-squared error in field estimation decreases as O(1/n) where n is the average number of samples collected by the mobile sensor. The average number of samples collected is determined by the inter-sample spacing distribution in the renewal process. An algorithm to ascertain spatial field's bandwidth is detailed, which works with high probability as the average number of samples n increases. This algorithm works in the same setup, i.e., in the presence of measurement-noise and unknown sampling locations.

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Bandlimited field reconstruction from samples obtained on a discrete grid with unknown random locations

Abstract: 1 This may arise in scenarios where location information is masked to preserve the identity of the sensors, or to reduce the amount of data that needs to be transmitted.

Cited by 3 publications

References 20 publications

Spatial Field estimation from Samples taken at Unknown Locations generated by an Unknown Autoregressive Process

Spatial Field estimation from Samples taken at Unknown Locations generated by an Unknown Autoregressive Process

Bandlimited field estimation from samples recorded by a location-unaware mobile sensor

On Bandlimited Field Estimation from Samples Recorded by a Location-Unaware Mobile Sensor

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